Write each number in standard form a+bi. -6-√-24 / 2

검증된 단계별 안내

Recognize that the expression involves a complex number because of the square root of a negative number: \(\sqrt{-24}\).

Rewrite the square root of the negative number using imaginary unit \(i\), where \(i = \sqrt{-1}\). So, \(\sqrt{-24} = \sqrt{24} \cdot i\).

Simplify \(\sqrt{24}\) by factoring it into \(\sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}\), so \(\sqrt{-24} = 2\sqrt{6}i\).

Substitute back into the original expression: \(\frac{-6 - 2\sqrt{6}i}{2}\).

Separate the fraction into real and imaginary parts: \(\frac{-6}{2} - \frac{2\sqrt{6}i}{2}\), then simplify each part to write the expression in standard form \(a + bi\).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Complex Numbers and Imaginary Unit

Complex numbers are expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit with the property i² = -1. Understanding how to represent square roots of negative numbers using i is essential for rewriting expressions involving √-24.

Simplifying Square Roots of Negative Numbers

To simplify the square root of a negative number, separate it into the square root of the positive part and the imaginary unit i. For example, √-24 can be written as √24 * i, and then further simplified by factoring 24 into perfect squares.

Algebraic Simplification and Division of Complex Expressions

When dividing expressions involving complex numbers, apply algebraic rules carefully, including distributing division over addition or subtraction and simplifying numerator and denominator separately. This helps in rewriting the expression in the standard form a + bi.